1

A boy goes to school from his house. On 1/4th on his way to school, he crosses a machinery station. And on 1/3rd on his way to his school, he crosses a Railway station. If he crossed the machinery station at 7:30 a.m. and the Railway station at 7:35 a.m. then how much time does he takes to reach the school?

2

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed. [CAT 2005]

At what time do Ram and Shyam first meet each other?

3

Two friends A and B start running simultaneously on a circular track at point X. If the length of the circular track is 360 m and the speed of A and B are 12 m/s and 18 m/s, then in how much time would they meet once again at the starting point X running in the same direction?

4

Three friends P, Q and R were standing on a circular track at point X running a race at the speed. If the length of the circular track is 480 m and the speed of P, Q and R are 8 m/s 6 m/s and 12 m/s, then in how much time would they meet once again at the starting point X?

5

There is a circular track of length of 440 m. There are three persons Symonds, Harbhajan and Inzamam standing at different points of the circular track ready to start the race with the speed of 5 m/s, 10 m/s and 8 m/s respectively. Symonds and Harbhajan are standing diagrammatically opposite to each other, while Inzamam is exactly in the mid-way between Symonds and Harbhajan, such that Symonds, Inzamam and Harbhajan are standing in the clockwise order. The race started at 10:00 A.M. All the three run in clockwise direction.

At what time would Inzamam and Symonds meet for the first time?

6

There are two places X and Y, 200 km apart from each other. Initially two persons P and Q are both at ‘X’. The speed of P is 20 kmph and Q is 30 kmph. Later on they starts to move to and fro between X and Y. 

If they starts to move between X and Y, then for the first time when they will meet each other?

7

 There are two places X and Y, 200 km apart from each other. Initially two persons P and Q are both at ‘X’. The speed of P is 20 kmph and Q is 30 kmph. Later on they starts to move to and fro between X and Y.

If they meet for the first time at a point M somewhere between X and Y, then what is the distance travelled by P to reach M?

8

Rajesh walks to and fro to a shopping mall. He spends 30 minutes shopping. If he walks at speed of 10 km an hour, he returns to home at 19.00 hours. If he walks at 15 km an hour, he returns to home at 18.30 hours. How fast must he walk in  order to return home at 18.15 hours?      [XAT 2009]

9

Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

10

Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?